Ikea TRADFRI remote button (square, ref E1743)

I know this device cannot be integrated with HE because it's Touchlink based and HE does not support that. It is of course supported by Ikea hub and it is also possible to pair it the Hue Bridge and have it control Hue lamps and at the same time, the Hue Bridge will still control the lamp.

Using any of the Hue Bridge integrations (Native, CoCoHue or Armand's), is it possible to control an Ikea or Hue outlet with the HE whilst simultaneously maintaining control of that outlet with the Ikea button? Directly in HE, I can't do this: if I pair the Ikea outlet with the button, it works but if I pair the outlet with HE, the button no longer works and vice-versa. I'm trying to do this, even if I need to buy a Hue Bridge.